A small rocket is launched vertically upward from the edge of a dit 128 f offthe

Question

A small rocket is launched vertically upward from the edge of a dit 128 f offthe ground at a speed of 96 Its height above the ground is given by the function 16+961 128, where t represents time measured in seconds. a. Assuming the rocket is launched at t-O, what is an appropriate domain for h? b. Graph h and delermine the time at which the rocket reaches its highest point. What is the height at that time? b. Which is the correot graph of h? A. 10 The rocket reaches its highest point at when t 272

Explanation / Answer

h(t) = -16 t2 + 96t + 128

h '(t) = -32t + 96

h ''(t) = -32 <0, so height is maximum

h '(t) =0

-32t + 96 =0

t =3 seconds

h(3)= -16(3)2+96(3) + 128 = 272 ft

The rocket reaches its highest point at when t = 3 .

Please put 3 in place of 272

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